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Solving for the Unknown: A Step-by-Step Guide to Isolating $k$ in the Equation $\frac{96}{k}=3$

In mathematics, solving equations is a fundamental concept that helps us understand the relationships between variables. One of the most common types of equations is the linear equation, which can be solved using various techniques. In this article, we will focus on solving the equation $\frac{96}{k}=3$ for the unknown variable $k$. We will break down the solution into manageable steps, making it easy to follow and understand.

Understanding the Equation

The given equation is $\frac{96}{k}=3$. To solve for $k$, we need to isolate the variable $k$ on one side of the equation. The equation can be rewritten as $96 = 3k$, where $k$ is the unknown variable.

Step 1: Multiply Both Sides by $k$

To isolate $k$, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $k$. This will eliminate the fraction and give us a simpler equation to work with.

$\frac{96}{k} \cdot k = 3 \cdot k$

Simplifying the equation, we get:

$96 = 3k$

Step 2: Divide Both Sides by 3

Now that we have the equation $96 = 3k$, we can solve for $k$ by dividing both sides of the equation by 3. This will give us the value of $k$.

$\frac{96}{3} = \frac{3k}{3}$

Simplifying the equation, we get:

$32 = k$

In this article, we solved the equation $\frac{96}{k}=3$ for the unknown variable $k$. We broke down the solution into manageable steps, making it easy to follow and understand. By multiplying both sides of the equation by $k$ and then dividing both sides by 3, we were able to isolate $k$ and find its value.

$k = 32$

• To solve for $k$ in the equation $\frac{96}{k}=3$, we can also use the method of cross-multiplication. This involves multiplying both sides of the equation by $k$ and then multiplying both sides by 3.
• If the equation is $\frac{96}{k}=x$, where $x$ is a variable, we can solve for $k$ by multiplying both sides of the equation by $k$ and then dividing both sides by $x$.
• To solve for $k$ in the equation $\frac{96}{k}=3$, we can also use the method of substitution. This involves substituting a value for $k$ into the equation and then solving for the value of $k$.

Solving equations like $\frac{96}{k}=3$ has many real-world applications. For example, in physics, we can use equations like this to solve problems involving motion and energy. In finance, we can use equations like this to solve problems involving interest rates and investments.

• One common mistake when solving equations like $\frac{96}{k}=3$ is to forget to multiply both sides of the equation by $k$.
• Another common mistake is to forget to divide both sides of the equation by 3.
• To avoid these mistakes, it's essential to carefully read and understand the equation before solving it.

In conclusion, solving the equation $\frac{96}{k}=3$ for the unknown variable $k$ is a straightforward process that involves multiplying both sides of the equation by $k$ and then dividing both sides by 3. By following these steps, we can easily isolate $k$ and find its value.
Solving for the Unknown: A Q&A Guide to Isolating $k$ in the Equation $\frac{96}{k}=3$

In our previous article, we solved the equation $\frac{96}{k}=3$ for the unknown variable $k$. We broke down the solution into manageable steps, making it easy to follow and understand. In this article, we will provide a Q&A guide to help you better understand the solution and answer any questions you may have.

Q: What is the equation $\frac{96}{k}=3$ trying to solve for?

A: The equation $\frac{96}{k}=3$ is trying to solve for the unknown variable $k$. We want to find the value of $k$ that makes the equation true.

Q: Why do we need to multiply both sides of the equation by $k$?

A: We need to multiply both sides of the equation by $k$ to eliminate the fraction. This will give us a simpler equation to work with.

Q: Why do we need to divide both sides of the equation by 3?

A: We need to divide both sides of the equation by 3 to isolate $k$. This will give us the value of $k$.

Q: What if the equation is $\frac{96}{k}=x$, where $x$ is a variable? How do we solve for $k$?

A: If the equation is $\frac{96}{k}=x$, where $x$ is a variable, we can solve for $k$ by multiplying both sides of the equation by $k$ and then dividing both sides by $x$.

Q: What if the equation is $\frac{96}{k}=3$, but we want to solve for $k$ in terms of $x$? How do we do it?

A: If the equation is $\frac{96}{k}=3$, but we want to solve for $k$ in terms of $x$, we can use the method of substitution. We can substitute a value for $k$ into the equation and then solve for the value of $k$.

Q: What are some common mistakes to avoid when solving equations like $\frac{96}{k}=3$?

A: Some common mistakes to avoid when solving equations like $\frac{96}{k}=3$ include forgetting to multiply both sides of the equation by $k$ and forgetting to divide both sides of the equation by 3.

Q: How do we know if the solution is correct?

A: To know if the solution is correct, we can plug the value of $k$ back into the original equation and check if it is true.

Q: What are some real-world applications of solving equations like $\frac{96}{k}=3$?

A: Solving equations like $\frac{96}{k}=3$ has many real-world applications, including physics, finance, and engineering.

In conclusion, solving the equation $\frac{96}{k}=3$ for the unknown variable $k$ is a straightforward process that involves multiplying both sides of the equation by $k$ and then dividing both sides by 3. By following these steps and avoiding common mistakes, we can easily isolate $k$ and find its value. We hope this Q&A guide has helped you better understand the solution and answer any questions you may have.

$k = 32$

• To solve for $k$ in the equation $\frac{96}{k}=3$, we can also use the method of cross-multiplication. This involves multiplying both sides of the equation by $k$ and then multiplying both sides by 3.
• If the equation is $\frac{96}{k}=x$, where $x$ is a variable, we can solve for $k$ by multiplying both sides of the equation by $k$ and then dividing both sides by $x$.
• To solve for $k$ in the equation $\frac{96}{k}=3$, we can also use the method of substitution. This involves substituting a value for $k$ into the equation and then solving for the value of $k$.

Solving equations like $\frac{96}{k}=3$ has many real-world applications, including physics, finance, and engineering. For example, in physics, we can use equations like this to solve problems involving motion and energy. In finance, we can use equations like this to solve problems involving interest rates and investments.

• One common mistake when solving equations like $\frac{96}{k}=3$ is to forget to multiply both sides of the equation by $k$.
• Another common mistake is to forget to divide both sides of the equation by 3.
• To avoid these mistakes, it's essential to carefully read and understand the equation before solving it.